The least bad option is stopping the bombings. Japan was at a point when kamikaze attacks didn't do shit to the navy sitting on their shores. Time had been bought, oil was nonexistent. The horrors of the firebombing of Tokyo dont make the nukes justified. You can cease bombings during negotiations.

And the time before the bomb dropped was the correct time, the Soviets had entered the war against Japan, Japan's chance at negotiating through a third party was now gone and the walls where closing in. This was the plan. The Soviets stayed out until that point with the intention of the Allies being literally to use that as leverage. The door was left open on purpose

https://books.google.com/books?id=rddhxSKGQ9oC&dq=soviet+neutrality+pact+1941+denounce&pg=PA150#v=onepage&q=soviet%20neutrality%20pact%201941%20denounce&f=false

The US drops the first bomb August 6th, August 7th the USSR declares war on Japan (technically telling Japan on the 8th and with the caveat that the USSR would consider itself at war from the 9th on). So yeah I'm gonna go with prior to the Soviets entering the war as per the United States own wishes, as the ideal time for negotiations. The US had broken Japan's codes and was reading messages like this from Ambassador Sato

"There is no alternative but immediate unconditional surrender if we are to prevent Russia's participation in the war."